A006898 a(n) = Sum_{k=0..n} C(n,k)*2^(k*(k+1)/2).

1, 3, 13, 95, 1337, 38619, 2310533, 283841911, 70927591153, 35812691480115, 36383765777442685, 74185239630793429775, 303119284294591169426729, 2479814853198140771706795531, 40599509058360322571947638063605

Offset: 0

Author

Colin Mallows

Keywords

• nonn

Comments

First differences of A006896.

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A006896, A006897, A135748.

Programs

Mathematica

Table[Sum[Binomial[n,k]2^((k(k+1))/2),{k,0,n}],{n,0,20}] (* Harvey P. Dale, Apr 01 2023 *)

PARI

a(n)=sum(k=0,n,binomial(n,k)*2^(k*(k+1)/2)) \\ Paul D. Hanna, Apr 10 2009

Formula

a(n) ~ 2^(n*(n+1)/2). - Vaclav Kotesovec, Nov 27 2017

Extensions

Formula and more terms from Vladeta Jovovic, Sep 20 2003

Edited by N. J. A. Sloane, Apr 12 2009 at the suggestion of Vladeta Jovovic